APRIL 1937 103

ALTERNATING-CURRENT CIRCUITS FOR DISCHARGE LAMPS

By E. G. DORGELO.

Summary. In contradistinction to the incandescent electric lamp, the gas discharge lamppossesses electrical characteristics which are entirely different for those of an ordinaryresistance. Therefore, when calculating the data for a proposed installation of gas dischargelamps modified methods must be employed; these are discussed in some detail in thisarticle. The characteristics of the simplest lamp installation, consisting of a gas dischargelamp with a choke coil connected in series with it, are analysed as an example.

Introduetion

A fundamental difference between gas dischargelamps and incandescent electric lamps is that theformer must always be connected to the mainssupply through a current-limiting device.In its simplest form this component consists of a

series resistance or a choking coil which limits thecurrent passing through the lamp. If the runningor starting voltage of the lamp is higher than themains voltage, a transformer which can be builtin with the choke must be inserted in the circuit.A so-called leakage transformer with the sameelectrical characteristics can also be used in placeof the transformer connected in series with a choke.The current-limiting device not only limits the

current intensity but also modifies the characterofthe current. It is useful to know also the variationsin the intensity and character of the current with

Sodium lamp

Mercurylamp SP

alteration in the characteristics of the lamp orwith fluctuations in mains voltage; a detailedknowledge of the method of operation of the current-limiting device is also desirable to enable its dimen-sions to bc kept small and its manufacture inex-pensive.

A brief survey is given below of the principalpoints which have to be considered in arriving atthe electrical specification of discharge lamps andtheir current-limiting devices; it is also shown how- by adopting certain simplifications - the elec-trical characteristics of an installation can becalculated. It "rill be seen that each individualrequirement of lamp voltage, power factor, thesensitivity of the lamp to voltage fluctuations,duration of the heating-up period, etc., introducesits own particular set of conditions, which cannotalways be satisfied simultaneously, so that fre-quently a oompromise must be made. These

Neon lamp

Mercurylamp HP

21103

Fig. 1. Voltage and current as a function of time for a sodium lamp, a neon lamp, a water-cooled SP mercury lamp and an air-cooled HP mercury lamp. Current commences toflow when the voltage has reached ED; during the passage of current the voltage remainsconstant (to a first approximation) at EB'

104 PHILIPS TECHNICAL REVIEW Vol. 2, No. 4

limitations are in part due to the simplicity ofthe circuit discussed here and which consists ofa choke coil in series with the lamp. If, on the,other hand, more complex circuits are used, anumber of possibilities arise which cannot hediscussed in this article.

,' Mathematical Simplifications

The following simplifications will be taken as thebasis of our analysis:1) The choke coil is assumed to combine a constant

'self-inductance L with an ohmic resistance R.2) The ma~s voltage is assumed to be sinusoidal

(with' an instantaneous value of E sin wt). '3) While the lamp remains burning, the voltage

applied to the lamp is taken to be constant(EB) with the current in opposition to it. Toensure that the lamp burns during each half-cycle, the voltage at its terminals must howeverfirst reach a value which is greater' 'than EBand which will be termed the striking voltàgeED" . . '

The va;iation in the voltage as a function ofthe time is plotted in fig. 1 for sodium, mercuryand neon lamps. While the 'assumption that therunning voltage is constant was found to be truein the case of mercury lamps, with sodium lampson the other hand the oscillogram reveals a dimi-.nution of this voltage at the beginning and endof each half-cycle. But for most calculations itwas found permissible to ascribe a constant me~nvalue to the running voltage in these cases also.

Final Mains Current and Consumption Current~

r:t:he inductive circuit described below is shownin diagrammatic form in fig. 2. It is assumed thatthe mains .voltage (E sin w t) is applied when .its

20925

Fig. 2. The circuit under discussion. The lamp and chokecoil are connected in series and the mains voltage E sin to tis applied. The chokecoil has self-inductance L and resistance R,

instantancous value is just zero (w t = 0); nocurrent ,then passes through the choke coil andthe 'lamp. Only when E sin w t = ED (which is onlypossible when E> ED), does ignition take placeand a current is able to pass. The lamp thus behaveslike.a switch which is operated at the moment whenE sin w t = ED' ' ...

Wethen have:

. EDW t = arc SIn -'

E

This value of w t will he denoted by a. Ifwe continueto compare the lamp with a switch, we must alsoassume that on closing the switch the circuitabsorbs an e.m.f, with a value of ED and a polarityin opposition to the applied mains voltage. Fig. 3

1Esin GJt

r

r 00000000' Is

s.;!--I ~1-.1~-;:O--'!J2~

Fig. 3. Equivalent circuit for the lamp. An e.m.f, EB whichcan be applied by closing the switch takes the place of thedischarge lamp.

shows the equivalent circuit of the lamp describedabove. SWitch S is closed as soon as the absolutevalu~ of the voltage exceeds ED and remains closeduntil the current changes sign and becomes zero.. The voltage equilibrium obtaining in the equiv-alent circuit after closing the switch can beexpressed by the equation:

. diE sin w t =, L R + L - + En.

dt

Solving this' equation for i wc get:

i = is + iv, where

. (1)

Here

z = YR2 + (w L)2 (total impedance),

wL'ljJ=arctan]i'

If. in the equivalent circuit (fig. 3) the switch.were kept closed for any arbitrarily long period,the current intensity iv would become very smallafter a certain time (lim iv = 0). The current thenflowing is given by:

. .' E . . EBL = L = - sm (w t -111') - - .1=," s Z -r R

is is therefore termed the final current. As may beseen i. is compounded of an :A.C. component given-by the mains voltage divided by the impedance of

APRIL 1937 CIRCUITS FOR DISCHARGE LAMPS 105

the circuit, and a D.C. component determined bythe direct voltage EB and the resistance R.At the moment of closing the circuit (w t = a),

is will as a rule not become' zero immediately.In this case t,he compensation current i, ensuresthat no resultant current flows when the circuit

, ,

is closed. Circuits are frequently encountered inelectricity in which the circuit-closing phenomenaoccurring are of a transient nature. This is howevernot the case with gas discharges. Ignition is repeatedtwice in each cycle and the circuit-closing phenom-ena here have a continuous effect on the currentcurve, as will be further shown below.

Periodical Ignition and Extinction

As already indicated the switch S in the equivalentcircuit (fig. 3) is opened the instant the currentbecomes 'zero '(w t = (3). It is shown in fig. 4 that

.,.:

'fÓ.R - ....; ..........-......----...... -IV_-.....

20927

Fig. 4. Current intensity through the lamp, The final mainscurrent derived from the mains voltage E sin m t and the

, impedance Z is represented by: '.. E. . EBls =z sm (mt-,p)-lf

and the compensation current by:

[EB E ] s. (a-oolj

i = --- sin (a-'1') e ooL• R Z , .

The hatched ordinates between the curves is and iv representsthe current intensity i. In the case illustrated the dischargeperiod is exactly half a cycle, (f3 = a + n). '

the current rapidly becomes zero, in fact so quicklythat no marked diminution in iv as yet takes place,When the current has once become zero, it remainsat this value until the absolute value of the mainsvoltage has again attained the value ED' During tbisinterval, whicli may be termed the re-ignition inter-val (j; not only is i= 0 but also di/dt =O. The onlyvoltage remaining 'i~ then the mains voltage andït also' detër~llies th'e instant of re-ignition. I~general the polarity of the mains voltage is then

reversed; after re-ignition we can 'again make use'of our equivalent circuit diagram, although' nowthe switch must be closed in the opposite direction.It is evident that the expression which we now

obtain for the current again contains the two'components is and ivo iv is again determined by'the tondition that at the instant of re-ignition,i = O. Hence contrary to 'circuits which do notcontain a dischargelamp, the compensation currentnever entirely disappears here. It is this componentwhich gives the current a permarient, non-sinusoidalcharacter. .

If the voltage ED at which' the lamp commencesto burn is constant, re-ignition occurs when w t = a,a + n, a + 2 n, etc. The expressions for is and i.. ,.are the same in all half-cycles, apart from the sign.To determine the character of the current it istherefore sufficient to, consider a single half-cycle.

Discharge Interval and Dark Interval :

.We shall now return to equation (1). To simplifyfurther analysis it will be àssumed that R can' be'neglected with reference to C9 L. The equation givingthe current 'can then be derived from' equation (1) ,by expanding the power function as a series, sothat at the' limit !J. ~ 0 only the first two termsremain. We then get:

.: wIL [E (cos a~c~s w"t) + EB(a~ t)]. (2)

By éalculation or by means of the constructionshown in fig. 5, the instant (w t = (3) can then bedetermined at which i becomes zero for, the fitst"time. Fig. 5 shows that the value of (3 is determinedby ED and EB and that the discharge interval((3 - a) can be both, longer and shorter' th~n ahalf-cycle, '.If f3 - a < n the current will remain zero for

a finite interval after extinction has taken place

. ,

"

Fig. 5. The same diagramas fig.4., but for R == 0, i.e. Z =m L.The e-function is resolved into a straight line with the slopeEB/m L. '

and until re-ignition of the .lamp takes place -in _..... ,. -,the opposite direction. The dark interval is givenby (j = n - W - a). Except for their algebraical

106 PHILIPS TECHNICAL REVIEW Vol. 2, No. 4

signs the voltages and currents are exactly thesame in the second half-cycle as in the first.If (3 - a = n, the dark interval disappears, as

is generally desirable, since the lamp radiates very'little light during this period and will he subjectto much less flickering when the dark interval iseliminated.

Consider now the case when ,(3 -.$I > n. It isseen that in this case also the lamp is immediatelyre-ignited in the opposite direction after extinction.The voltage at the instant re-ignition takes placeis now greater than ED in the negative phase, whilein the positive phase' the voltage is exactly equalto ED' The characters of the two phases are thereforenot identical. Fig. 6 shows a sequence of half-cycleswhere it is apparent that the positive phase islonger and the negative phase shorter than ahalf-cycle. The sum of a positive and a negativephase is however slightly longer than" a wholecycle, so that the variation of the current is not

cv t =, fJ ~ n + a,

where the sign of equality applies when the darkinterval is zero. On inserting this value of cv t Inequation (2) we get:,

. . .'. (3)

the sign of equality again applying to the absenceof a dark interval. .

The voltage E. at the ins,tant of re-ignition how-ever satisfies the following equation which can he

, readily deduced from fig. 6:

Es ' ED-::::::::-E :?' E'sin a . . . (4)

where the sign of equality now implies the existenceof a dark interval, i.e. for just the. converse caseto that for which equation (3) is valid. We thusarrive at the following scheme:

Fig. 6. The same diagram as fig. 5, 'but expanded. to a number of periods. If the firstdischarge lasts longer than a half-cycle (fullline) the third discharge will be shorter thanthe first, the fifth shorter than the third, and so on: The full Iine gradually approachesthe dash line which represents the equilibrium condition in which the duration of thedischarge is exactly haIf a cycle.At this equilibrium thevoltage E. available for re-ignitionis greater than ED' , , '. "

:

"

periodic. As shown in the figure, the times ofignition are displaced progressively such that theequilibrium condition indicated by the dash lineis attained. In this state the two half-phases areidentical and are equal to a half-cycle. The voltageE at the instant .of re-ignition is the same for both.half-cycles in this - equilibrium . condition and is'greater than the striking voltage ED'

We thus arrive at the conclusions that the mainsvoltage may exceed the striking voltage at theinstant the lamp is re-ignited. The excess valueof the mains voltage is a measure of the reliabilityof re-ignition.

It i~ therefore important to know whether atgiven values of EB, ED and E the dark interval canbe zero or not.' The criterion for this is determinedas follows.

Substituting cv t a in equation (2), we get asrequired i = O. At the instant cv t = fJ whereagain i 0 we get for the equilibrium state:

With interval Interval just zero No interva'l

ED sin aED sin a

EDsina=- =E >-, E E

nEB nEB n Encos a = 2E cos a = -- cos a <2E2 E

(nEBr (EDr (nEBr (EDr (nEBr '(EDr2E + E >1,2 E + E =1 '2 E + E <1

The.third line in this table is obtained by squaringand adding the first twó equations. It is found thatthe following expression may he taken as thecriterion for immediate re-ignition:

If the sign of equality applies, then a is determinedboth by the discharge interval given by equation (3)

APRIL 1937 CIRCUITS FOR DISCHARGE LAMPS 107

and by the dark interval given by equation (4);where the sign < applies, a is determined by thedischarge interval alone, when E sin a > ED, -and

. the difference E sin a - ED may be taken as ameasU1:efor the reliability of re-ignition. _,1

Reliability of Re-ignition and Power Fact~r

It is interesting to examine what cases arisewhen EB and ED vary from' 0 to E either togetheror independently of each other.This _variation can in fact be examined in the

case of a mercury lamp, for on heating the lampthe pressure of the mercury increases and hencealso the values of EB and ED'At very low values of EBIE and EDIE, equation

(5) is definitely satisfied. It follows from equation(3) that a is approximately 90 deg 1). Ignition there-fore takes place when the mains voltage has almostreached its peak value. The reliability is thereforevery high.If _EB and ED increase, equation (3) indicates

. that a diminishes. Ignition is therefore obtainedrelatively earlier. The amount by which the m~insvoltage exceeds ED is gradually reduced arideventually becomes zero (fig. 7). On further raisingEB and ED, a'must again increase, and the instantof ignition is then no longer given by equation (3)but by equation (4), at the same time a' darkinterval is obta~ed. We have thus passedthroughthe minimum value of a. How small a can be madedepends on the ratio EDIEB, i.e. merely on the lamp.

Fig. 7. This diagram is based on oscillograms recording thevariation of the electrode voltage of a mercury lamp. Thefive exposures were made at short intervals during the heating-up of the lamp. The gradual increase in the striking and runningvoltages is indicated as well as the resulting displacementof the moment of ignition. In the case of an air-cooled mercurylamp this increase ceases before the striking voltage becomesgreater than the mains voltage at the moment of extinction.In the case of a water-cooled mercury lamp with which .theab~ve diagram was obtained, heating-up continues after thernainsvoltage is reached. A dark interval occurs, during whichthe voltage impressed on the lamp is exactly equal to themains voltage.

- 1) An extreme case occurs' when the lamp is short circuited;the current then passes through zero at the instant themains voltage just passes through its peak value.

If, for instance EDIEB =. 1, then it follows fromequation (5):

Hence EnlE = 0.536 and (cos a)mnx= 0.536 . nl2 =0.~4. With a higher ratio ofEDIEB the maximum'value which cos a can assume is naturally lower.

The greater the value of cos a the smaller will bethe phase displacement between the current; andthe mains voltage, in so f~r as one can speak ofa phase displacement in the case of a non-sinusoidalcurrent. It may therefore be expected that there, is a close relationship between the instant of ignitionand the power factor. For a sinusoidal current thepower factor is usually given as cos (/J, which wedefine as the ratio of the true power to the wattlcssor apparent power.

Limiting consideration to the case where thedark ~terval is zero, the power ,W is 'equal to therunning vçltage multiplied by the mean current .intensity during a half-cycle:

a+n1 -.W = EB . - -f i d (co t).

n'a

By means of equation (2) we can ~olvethe integral. and thus get:

and we get the expression:

VA = É . iEei! - (1.09 EB)2ei! roL, (7)

As the terms unde~ the root signs in (6) and (7)are almost the same, we have fOTthe power factor 17to a first approximation:

W EB,17 = - = 0.9 . - = 0.81 cos a.

VA " Eei!

In this circuit therefore the ratio of the running

108 PHILlPS TECHNICAL REVIEW Vol. 2, No. 4

voltage of the lamp to the effective mains voltage"is a measure of the power factor., In the case discussed above where the maximumvalue of cos a is realised, the maximum powerfactor is also obtained, "but is only 0.68. It hasindeed not been found possible to obtain a highervalue with the inductive circuit. Generally En/EBis greater than 1, which results in a still lo,~erpower factor. The power factor can be improvedby connecting a condenser, which compensates thewattless current component," in parallel with' thelamp and choke coil.

Choice of Running Voltage

When designing the combination consisting ofthe discharge lamp and the current limiting unit,the first point to be determined is the voltage

. which has to be applied to ""he lamp arid chokecoil. A preference is usually shown for direct con-nection to the mains (e.g. 220 volts for HO-mercurylamps). Other lamps can be run with better effi-ciency on higher voltages, in which case the mainsvoltage must be stepped up by transformation (e.g.440 volts for SO-sodium lamps, 600 volts for water-c~oled SP-mercury lamps). To obtain a maximumpower factor the running voltage is taken l:I,S highas possible for a specific mains voltage (when alsothe dimensions of the choke coil are reduced to aminimum).

Hitherto we have regarded the striking voltageEn as having a fixed value, being determined bythe characteristics of the lamp. Actually this is notthe case, for with all discharge lamps the voltagerequired for re-ignition increases during the darkinterval, as indicated in jig. 8 by the three thin

"Fig. 8. In the example shown here the mains"voltage at theinstant f3 is smaller than the voltage En required for re-ignition.It is therefore -necessary to wait until the mains voltage hasreached this value. In general the voltage required for ignitionincreases during this interval. 1, 2 and 3 represent points atwhich the mains voltage eventually predominates and startsthe discharge, while in 3 this does not occur and no re-ignitionresults. .

lines -, It may then occur that the instantaneousvalue of the mains voltage, which at the beginningof the dark interval is smaller than En, does not

increase sufficiently quickly to attain the voltagerequired for re-ignition, so that no re-ignition atall takes place (fig. 8, éase 3). To prevent thishappening the running and striking voltages of ,the lamp must not be made too high, sp thatcondition (5) specifying the absence of a darkinterval down to zero is satisfied.

Stability with respect' to Fluctuations in MainsVoltage.

The question of determining the lamp voltagehas been discussed in principle above; there arehowever a number of other factors which necessitatea modification of.the results arriv~d at.The chief of these is a fluctuation in the mains

voltage. With slow fluctuations the temperature ~fthe lamp also may change, which in mercury lampsresult in an alteration in the striking voltage. Thevariation of 'the latter is"in the same sense as thefluctuations in mains voltage (the static character-istic is positive); with sodium lamps these variationsare in opposite directions, If, for instance, the mainsvoltage drops, the striking voltage will rise, wherebyre-ignition becomes less reliable. In this case therunning voltage must therefore be taken lower thanrequired by equation (5) in order to preserve fullreliability in service."On. sudden variations in the mains voltage therunning voltage may vary also in the oppositedirection with mercury lamps (negative dynamiccharacteristic), so that again here it 'must be putslightly lower. Fluctuations in mains voltage affectalso the consumption of énergy and hence theluminous flux. By differentiating equation (6) (atconsta:t;tt EB) with respect to E.Jf we get for thepercentage variation of the power input:

dW 1 d E.ff .E.ff 'W

1- (1.11~rThe .percentage variation in power is thereforealways greater than the percentage variation inthe mains voltage, the difference being the greaterthe greater EB/E. If a considerable fluctuation in"W is to be avoided, then according to the lastequation, EB/E must be made too high. This again

" leads to the condition that the running voltageof the lamp should not be taken too high.Special 'importance attaches to the value of the

power absorbed with variation in the runningvoltage. With both mercury and sodium lamps,there is. a tendency for the running voltage toincrease with the time the lamp has been in use.

APRIL 1937 CIRCUITS FOR DISCHARGE LAMPS 109

This may result in a reduction in power consump- As already pointed out in a previous article 3),tion, in other words an increased reduction in the a minimum starting current is required for heating-luminous flux; there is, however, also the possibility up the lamp, which: is two to three times the normalthat the power consumption may also in~rease and .. lamp current. The starting current is roughly equalthe reduc~ion. in light referred to is then either to the short-circuit current ik ,of the current-partially or totally compensated. limiting component:

It follows from equation (6) that with an increaseof EB from 0 to E~{f, w at first increases, and laterbegins to diminish again. The maximum value isobtained at EB = 0.64 Ecff'If, for instance, E.ff = 220 V,. the power

consumption will increase with the age. of the lamp'for EB below 140 volts, while it will diminsh forEB above 140 volts 2).

Heating-up of High-Pressure Mercury ~amps

In conclusion. reference must be made to theheating-up of mercury lamps. After switching on'a certain time must elapse befor~ the voltage ac~ossthe mercury lamp has reached its full value (10 to15 mins with an HP lamp, 1/2 to 2 secs with awatercooled SP lamp).

2) If ED is greater than 1.57 EB' then for EB = 0.640E.ffthe condition that no dark interval shall occur is nolonger satisfied. Extending our analysis to include thiscase, we should get in place of equation (6) a generalisedexpression for. the power containing an independent

. variable in addition to EB and ED" This aspect of thesubject cannot be further p;i"rsü;;dhere,

. E'{f .~k=-'. Lro'

while the normal running current is;

. iE •.i - (1.09 EB)2~= --=-----roL

For ik greater than 2 i, we have EB> 0.79 E'ff' thusgiving in this case a minimum running voltage,which is so high that it conflicts with the require- .ments set out above. This difficulty may be over-come by using a choke coil during the heating-upperiod with a lower self-inductance than required

• for normal running. A method in general use forthis purpose provides a fairly high saturation ofthe iron in the series 'conn:ectëd 'choking coil, Theself-inductance then diminishes with increase inthe current intensity, such 'that the ~hort-circuitcurrent ik does actually reduce the impedance ofthe choke. ' '.

3) Philips techn: Rev .•,I, 129, :1;936.